Details

analyze1.1s (16.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample4.2s (63%)

Results

1.2s	1925×	body	1024	valid
988.0ms	1625×	body	1024	invalid
835.0ms	4936×	body	128	valid
411.0ms	936×	body	512	valid
402.0ms	875×	body	512	invalid
150.0ms	456×	body	256	valid
128.0ms	420×	body	256	invalid
123.0ms	628×	body	128	invalid
2.0ms	3×	body	2048	valid
1.0ms	1×	body	2048	invalid

preprocess25.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

96×	`fma-def_binary64`
70×	`*-commutative_binary64`
57×	`associate-/l*_binary64`
30×	`associate-/r/_binary64`
26×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	80
1	69	72
2	160	72
3	243	72
4	321	72
5	375	72
6	420	72
7	474	72
8	480	72
0	3	3
1	3	3

Stop Event

1×	unsound
1×	saturated

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
0
2

Call 2

Inputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))
(+.f64 (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (.f64 th th)) (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (.f64 a2 a2)))
(+.f64 (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (.f64 th th)))

Outputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (.f64 th th)) (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (+.f64 (.f64 th th) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (fma.f64 th th (.f64 a2 a2)))
(.f64 (cos.f64 a1) (/.f64 (fma.f64 th th (.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (.f64 th th)))
(.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 th th)))
(.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 th th)))
(.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (fma.f64 th th (.f64 a1 a1)))

Symmetry

(sort a1 a2)

Compiler

Compiled 22 to 15 computations (31.8% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

32×	`fma-def_binary64`
23×	`*-commutative_binary64`
20×	`associate-/l*_binary64`
11×	`associate-/r/_binary64`
9×	`associate-*r/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	27	18
2	58	18
3	88	18
4	115	18
5	135	18
6	152	18
7	170	18
8	172	18

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Outputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.5b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.6b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Compiler

Compiled 108 to 70 computations (35.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
✓	0.4b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

series15.0ms (0.2%)

Counts

2 → 60

Calls

15 calls:

Time	Variable		Point	Expression
3.0ms	th	@	inf	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
2.0ms	a2	@	inf	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
1.0ms	a1	@	0	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
1.0ms	a1	@	0	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
1.0ms	th	@	0	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

rewrite45.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

523×	`log-prod_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
182×	`pow3_binary64`
171×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	224	29
2	2729	29

Stop Event

1×	node limit

Counts

2 → 65

Calls

Call 1

Inputs
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 2)) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 a1 a2) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a1 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (hypot.f64 a1 a2) (cbrt.f64 2)) (/.f64 (hypot.f64 a1 a2) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) (.f64 2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) 1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (pow.f64 2 1/4)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (cos.f64 th) (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3) (pow.f64 (cos.f64 th) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))) 1))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 2)) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a1 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 a1 a2) (cbrt.f64 2)) (/.f64 (hypot.f64 a1 a2) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) (*.f64 2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) 1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (pow.f64 2 1/4)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (cos.f64 th) (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3) (pow.f64 (cos.f64 th) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))) 1))))))

simplify44.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

821×	`unswap-sqr_binary64`
650×	`associate-l_binary64`
423×	`fma-def_binary64`
199×	`associate-/l*_binary64`
171×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	1243
1	107	1175
2	286	1171
3	1023	1103
4	3816	1103

Stop Event

1×	node limit

Counts

125 → 87

Calls

Call 1

Inputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2)))))))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))

Outputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (sqrt.f64 2))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (.f64 -1/2 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th)))))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (fma.f64 -1/2 (/.f64 (.f64 th th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (.f64 a2 a2)))) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(fma.f64 -1/2 (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (.f64 th th)) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))
(fma.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (.f64 -1/2 (*.f64 th th)) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (fma.f64 -1/2 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th))) (.f64 1/24 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 4)))))))
(+.f64 (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (fma.f64 -1/2 (/.f64 (.f64 th th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (.f64 a2 a2)))) (.f64 1/24 (/.f64 (pow.f64 th 4) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (.f64 a2 a2)))))))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (fma.f64 -1/2 (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (.f64 th th)) (fma.f64 1/24 (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (pow.f64 th 4)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))))
(fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (+.f64 (.f64 1/24 (pow.f64 th 4)) (.f64 -1/2 (*.f64 th th))))))
(+.f64 (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2)))))))
(fma.f64 -1/720 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 6))) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (fma.f64 -1/2 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th))) (.f64 1/24 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 4))))))))
(+.f64 (+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (fma.f64 -1/2 (/.f64 (.f64 th th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (.f64 a2 a2)))) (.f64 1/24 (/.f64 (pow.f64 th 4) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (.f64 a2 a2))))))) (fma.f64 -1/720 (/.f64 (pow.f64 th 6) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2)))) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(+.f64 (fma.f64 -1/2 (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (.f64 th th)) (fma.f64 1/24 (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (pow.f64 th 4)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))) (fma.f64 -1/720 (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (pow.f64 th 6)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
(fma.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (.f64 -1/720 (pow.f64 th 6)) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (+.f64 (.f64 1/24 (pow.f64 th 4)) (.f64 -1/2 (*.f64 th th)))))))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (cos.f64 th))
(.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (cos.f64 th))
(.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (cos.f64 th))
(.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))

prune78.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	80	7	87
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	81	8	89

Error

0.0b

Counts

89 → 8

Alt Table

Status	Error	Program
	0.6b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))))
	0.5b	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
	0.6b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
	0.5b	(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.4b	(*.f64 (cos.f64 th) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
✓	0.5b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
▶	0.4b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))

Compiler

Compiled 1718 to 1136 computations (33.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 a1 a2)
✓	0.0b	(pow.f64 (hypot.f64 a1 a2) 2)
✓	0.1b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
✓	0.4b	(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2))

series32.0ms (0.5%)

Counts

4 → 108

Calls

27 calls:

Time	Variable		Point	Expression
4.0ms	a1	@	0	(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2))
4.0ms	a2	@	0	(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2))
4.0ms	th	@	inf	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
2.0ms	a1	@	inf	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
2.0ms	a1	@	0	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))

rewrite48.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

533×	`log-prod_binary64`
208×	`pow1/3_binary64`
207×	`expm1-udef_binary64`
207×	`log1p-udef_binary64`
189×	`pow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	42
1	249	40
2	2782	40

Stop Event

1×	node limit

Counts

4 → 105

Calls

Call 1

Inputs
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2))
(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
(pow.f64 (hypot.f64 a1 a2) 2)
(hypot.f64 a1 a2)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a1 a2) 2))) (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a1 a2) 2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a1 a2) 2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) (.f64 (sqrt.f64 1/2) 1/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (.f64 (sqrt.f64 1/2) 1/2) (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) (.f64 (sqrt.f64 1/2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (.f64 (sqrt.f64 1/2) 1/2) (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)))) (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 (cos.f64 th)) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/4))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)) 3) (pow.f64 (cos.f64 th) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)) 3) (pow.f64 (cos.f64 th) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 a1 a1) (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 a2 a2) (.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (hypot.f64 a1 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2))) (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (hypot.f64 a1 a2) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 a1 a2) (hypot.f64 a1 a2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (hypot.f64 a1 a2) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (hypot.f64 a1 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2) (.f64 (cbrt.f64 (hypot.f64 a1 a2)) (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 4)) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (hypot.f64 a1 a2)) (.f64 (sqrt.f64 (hypot.f64 a1 a2)) (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (hypot.f64 a1 a2)) 3) (sqrt.f64 (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (hypot.f64 a1 a2) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2)) (cbrt.f64 (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 a1 a1) 3) (pow.f64 (.f64 a2 a2) 3)) (fma.f64 (.f64 a1 a1) (.f64 a1 a1) (-.f64 (.f64 (.f64 a2 a2) (.f64 a2 a2)) (.f64 (.f64 a1 a1) (.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (.f64 (.f64 a2 a2) (.f64 a2 a2))) (-.f64 (.f64 a1 a1) (.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (hypot.f64 a1 a2) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (.f64 a1 a1)) (exp.f64 (.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (.f64 a2 a2)) (exp.f64 (.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 a1 a1 (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 a2 a2 (.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 a1 a1) (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 a2 a2) (.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 a1) 2) (.f64 (cbrt.f64 a1) a1) (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 a2) 2) (.f64 (cbrt.f64 a2) a2) (.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 a1) (.f64 (sqrt.f64 a1) a1) (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 a2) (.f64 (sqrt.f64 a2) a2) (.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (pow.f64 (cbrt.f64 a2) 2) (pow.f64 (cbrt.f64 a2) 2)) (pow.f64 (cbrt.f64 a2) 2) (.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (pow.f64 (cbrt.f64 a1) 2) (pow.f64 (cbrt.f64 a1) 2)) (pow.f64 (cbrt.f64 a1) 2) (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 a1 (sqrt.f64 a1)) (sqrt.f64 a1) (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 a2 (sqrt.f64 a2)) (sqrt.f64 a2) (.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 a2 (pow.f64 (cbrt.f64 a2) 2)) (cbrt.f64 a2) (.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 a1 (pow.f64 (cbrt.f64 a1) 2)) (cbrt.f64 a1) (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (hypot.f64 a1 a2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (hypot.f64 a1 a2))) (cbrt.f64 (exp.f64 (hypot.f64 a1 a2))))) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 a1 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 a1 a2)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 a1 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (hypot.f64 a1 a2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 a1 a2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (hypot.f64 a1 a2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2) (cbrt.f64 (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (hypot.f64 a1 a2)) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (hypot.f64 a1 a2)) (sqrt.f64 (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 a1 a2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 a1 a2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 a1 a2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (hypot.f64 a1 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (hypot.f64 a1 a2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (hypot.f64 a1 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (hypot.f64 a1 a2)) 1))))))

simplify81.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

850×	`times-frac_binary64`
413×	`fma-def_binary64`
221×	`associate-+r+_binary64`
207×	`+-commutative_binary64`
181×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	295	3724
1	960	3314
2	3541	3074

Stop Event

1×	node limit

Counts

213 → 198

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6))))) (.f64 5/64 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a1 8))) (+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6))))) (.f64 5/64 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a1 8))) (+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 12) (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 a2 8))) (.f64 -1/2 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a2 2)))) (pow.f64 a2 2))) (+.f64 (.f64 1/8 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a2 4))) (+.f64 (.f64 1/256 (/.f64 1 (pow.f64 a2 10))) (.f64 -1 (+.f64 (pow.f64 (/.f64 1/16 (pow.f64 a2 5)) 2) (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 a2 8))) (.f64 -1/2 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a2 2)))) (pow.f64 a2 2))) (.f64 1/8 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (*.f64 1/16 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a2 4))))))))))))))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
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(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (.f64 1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4))))))))
a2
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2)
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5))) a2)))
a1
(+.f64 a1 (*.f64 1/2 (/.f64 (pow.f64 a2 2) a1)))
(+.f64 a1 (+.f64 (.f64 -1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))) (.f64 1/2 (/.f64 (pow.f64 a2 2) a1))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5))) (+.f64 a1 (+.f64 (.f64 -1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))) (*.f64 1/2 (/.f64 (pow.f64 a2 2) a1)))))
(*.f64 -1 a1)
(+.f64 (.f64 -1 a1) (.f64 -1/2 (/.f64 (pow.f64 a2 2) a1)))
(+.f64 (.f64 -1 a1) (+.f64 (.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))) (*.f64 -1/2 (/.f64 (pow.f64 a2 2) a1))))
(+.f64 (.f64 -1 a1) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))) (.f64 -1/2 (/.f64 (pow.f64 a2 2) a1)))))
a1
(+.f64 a1 (*.f64 1/2 (/.f64 (pow.f64 a2 2) a1)))
(+.f64 a1 (+.f64 (.f64 -1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))) (.f64 1/2 (/.f64 (pow.f64 a2 2) a1))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5))) (+.f64 a1 (+.f64 (.f64 -1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))) (*.f64 1/2 (/.f64 (pow.f64 a2 2) a1)))))
a2
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2)
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5))) a2)))
(*.f64 -1 a2)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 a1 2) a2)) (.f64 -1 a2))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 a1 2) a2)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))) (*.f64 -1 a2)))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 a1 2) a2)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5))) (.f64 -1 a2))))

Outputs
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6))))) (.f64 5/64 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a1 8))) (+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(fma.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))) (/.f64 5/64 (pow.f64 a2 6))) (pow.f64 a1 8)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (fma.f64 (-.f64 (/.f64 5/64 (pow.f64 a2 6)) (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6)))) (pow.f64 a1 8) (fma.f64 a2 a2 (.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (fma.f64 (+.f64 (-.f64 (/.f64 5/64 (pow.f64 a2 6)) (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2)) (/.f64 -1/16 (pow.f64 a2 6))) (pow.f64 a1 8) (fma.f64 a2 a2 (.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6))))) (.f64 5/64 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a1 8))) (+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 12) (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 a2 8))) (.f64 -1/2 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a2 2)))) (pow.f64 a2 2))) (+.f64 (.f64 1/8 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a2 4))) (+.f64 (.f64 1/256 (/.f64 1 (pow.f64 a2 10))) (.f64 -1 (+.f64 (pow.f64 (/.f64 1/16 (pow.f64 a2 5)) 2) (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 a2 8))) (.f64 -1/2 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a2 2)))) (pow.f64 a2 2))) (.f64 1/8 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (*.f64 1/16 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a2 4))))))))))))))
(fma.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))) (/.f64 5/64 (pow.f64 a2 6))) (pow.f64 a1 8)) (fma.f64 (sqrt.f64 1/2) (.f64 a2 a2) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 (pow.f64 a1 12) (fma.f64 1/2 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 a2 8)) (.f64 1/2 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))) (.f64 a2 a2)))) (.f64 a2 a2)) (+.f64 (fma.f64 1/8 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))) (pow.f64 a2 4)) (/.f64 1/256 (pow.f64 a2 10))) (neg.f64 (+.f64 (pow.f64 (/.f64 1/16 (pow.f64 a2 5)) 2) (fma.f64 1/2 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 a2 8)) (.f64 1/2 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))) (.f64 a2 a2)))) (.f64 a2 a2)) (.f64 1/8 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))) (pow.f64 a2 4)))))))))))))
(+.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 (pow.f64 a1 12) (fma.f64 1/2 (-.f64 (/.f64 1/64 (.f64 (.f64 a2 a2) (pow.f64 a2 8))) (/.f64 (.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))) -1/2) (pow.f64 a2 4))) (-.f64 (fma.f64 1/8 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))) (pow.f64 a2 4)) (/.f64 1/256 (pow.f64 a2 10))) (fma.f64 1/2 (-.f64 (/.f64 1/64 (.f64 (.f64 a2 a2) (pow.f64 a2 8))) (/.f64 (.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))) -1/2) (pow.f64 a2 4))) (fma.f64 1/8 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))) (pow.f64 a2 4)) (pow.f64 (/.f64 1/16 (pow.f64 a2 5)) 2)))))))) (.f64 (sqrt.f64 1/2) (fma.f64 (-.f64 (/.f64 5/64 (pow.f64 a2 6)) (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6)))) (pow.f64 a1 8) (.f64 a2 a2))))
(+.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 (pow.f64 a1 12) (fma.f64 1/2 (-.f64 (/.f64 1/64 (.f64 (.f64 a2 a2) (pow.f64 a2 8))) (/.f64 (.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))) -1/2) (pow.f64 a2 4))) (-.f64 (fma.f64 1/8 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))) (pow.f64 a2 4)) (/.f64 1/256 (pow.f64 a2 10))) (fma.f64 1/2 (-.f64 (/.f64 1/64 (.f64 (.f64 a2 a2) (pow.f64 a2 8))) (/.f64 (.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))) -1/2) (pow.f64 a2 4))) (fma.f64 1/8 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))) (pow.f64 a2 4)) (pow.f64 (/.f64 1/16 (pow.f64 a2 5)) 2)))))))) (.f64 (sqrt.f64 1/2) (fma.f64 (+.f64 (-.f64 (/.f64 5/64 (pow.f64 a2 6)) (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2)) (/.f64 -1/16 (pow.f64 a2 6))) (pow.f64 a1 8) (.f64 a2 a2))))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (+.f64 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4)))) (pow.f64 a1 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(fma.f64 (sqrt.f64 1/2) (.f64 a2 a2) (+.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (/.f64 (sqrt.f64 1/2) (/.f64 (.f64 a1 a1) (*.f64 (pow.f64 a2 4) 0)))))
(+.f64 (.f64 (/.f64 (sqrt.f64 1/2) a1) (/.f64 0 a1)) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) 0)
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (+.f64 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4)))) (pow.f64 a1 2)) (+.f64 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (pow.f64 a2 6)) (.f64 -1/8 (pow.f64 a2 6)))) (pow.f64 a1 4)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))))
(fma.f64 (sqrt.f64 1/2) (.f64 a2 a2) (+.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (/.f64 (sqrt.f64 1/2) (/.f64 (.f64 a1 a1) (*.f64 (pow.f64 a2 4) 0)))))
(+.f64 (.f64 (/.f64 (sqrt.f64 1/2) a1) (/.f64 0 a1)) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) 0)
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (+.f64 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4)))) (pow.f64 a1 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(fma.f64 (sqrt.f64 1/2) (.f64 a2 a2) (+.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (/.f64 (sqrt.f64 1/2) (/.f64 (.f64 a1 a1) (*.f64 (pow.f64 a2 4) 0)))))
(+.f64 (.f64 (/.f64 (sqrt.f64 1/2) a1) (/.f64 0 a1)) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) 0)
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (+.f64 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4)))) (pow.f64 a1 2)) (+.f64 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (pow.f64 a2 6)) (.f64 -1/8 (pow.f64 a2 6)))) (pow.f64 a1 4)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))))
(fma.f64 (sqrt.f64 1/2) (.f64 a2 a2) (+.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (/.f64 (sqrt.f64 1/2) (/.f64 (.f64 a1 a1) (*.f64 (pow.f64 a2 4) 0)))))
(+.f64 (.f64 (/.f64 (sqrt.f64 1/2) a1) (/.f64 0 a1)) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) 0)
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (+.f64 (.f64 (+.f64 (.f64 -1 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 a1 6))) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2))) (.f64 5/64 (/.f64 1 (pow.f64 a1 6)))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 8))) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(fma.f64 (sqrt.f64 1/2) (.f64 a2 a2) (fma.f64 (fma.f64 -1 (+.f64 (/.f64 1/16 (pow.f64 a1 6)) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2)) (/.f64 5/64 (pow.f64 a1 6))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 8)) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 8) (-.f64 (/.f64 5/64 (pow.f64 a1 6)) (+.f64 (/.f64 1/16 (pow.f64 a1 6)) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2))))) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 8) (-.f64 (+.f64 (/.f64 5/64 (pow.f64 a1 6)) (/.f64 -1/16 (pow.f64 a1 6))) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2)))) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))))
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(fma.f64 (sqrt.f64 1/2) (.f64 a2 a2) (fma.f64 (sqrt.f64 1/2) (.f64 (fma.f64 1/2 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 a1 8)) (.f64 1/2 (/.f64 (+.f64 (/.f64 1/16 (pow.f64 a1 6)) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2)) (.f64 a1 a1)))) (.f64 a1 a1)) (fma.f64 1/8 (/.f64 (+.f64 (/.f64 1/16 (pow.f64 a1 6)) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2)) (pow.f64 a1 4)) (fma.f64 -1 (+.f64 (pow.f64 (/.f64 1/16 (pow.f64 a1 5)) 2) (fma.f64 1/2 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 a1 8)) (.f64 1/2 (/.f64 (+.f64 (/.f64 1/16 (pow.f64 a1 6)) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2)) (.f64 a1 a1)))) (.f64 a1 a1)) (.f64 1/8 (/.f64 (+.f64 (/.f64 1/16 (pow.f64 a1 6)) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2)) (pow.f64 a1 4))))) (/.f64 1/256 (pow.f64 a1 10))))) (pow.f64 a2 12)) (fma.f64 (fma.f64 -1 (+.f64 (/.f64 1/16 (pow.f64 a1 6)) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2)) (/.f64 5/64 (pow.f64 a1 6))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 8)) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)))))
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(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (+.f64 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4))) (cos.f64 th))) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 (.f64 a1 a1) (cos.f64 th)) (.f64 (.f64 a2 a2) (cos.f64 th)))) (/.f64 (sqrt.f64 1/2) (/.f64 (.f64 a1 a1) (.f64 (.f64 (pow.f64 a2 4) 0) (cos.f64 th)))))
(fma.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (.f64 (/.f64 (sqrt.f64 1/2) a1) (/.f64 (.f64 (cos.f64 th) 0) a1)))
(fma.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) 0)
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (+.f64 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4))) (cos.f64 th))) (pow.f64 a2 2)) (+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))) (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 1/8 (pow.f64 a1 6)) (.f64 -1/8 (pow.f64 a1 6))) (cos.f64 th))) (pow.f64 a2 4)))))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 (.f64 a1 a1) (cos.f64 th)) (.f64 (.f64 a2 a2) (cos.f64 th)))) (/.f64 (sqrt.f64 1/2) (/.f64 (.f64 a1 a1) (.f64 (.f64 (pow.f64 a2 4) 0) (cos.f64 th)))))
(fma.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (.f64 (/.f64 (sqrt.f64 1/2) a1) (/.f64 (.f64 (cos.f64 th) 0) a1)))
(fma.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) 0)
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a2 a2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (+.f64 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4))) (cos.f64 th))) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 (.f64 a1 a1) (cos.f64 th)) (.f64 (.f64 a2 a2) (cos.f64 th)))) (/.f64 (sqrt.f64 1/2) (/.f64 (.f64 a1 a1) (.f64 (.f64 (pow.f64 a2 4) 0) (cos.f64 th)))))
(fma.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (.f64 (/.f64 (sqrt.f64 1/2) a1) (/.f64 (.f64 (cos.f64 th) 0) a1)))
(fma.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) 0)
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (+.f64 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4))) (cos.f64 th))) (pow.f64 a2 2)) (+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))) (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 1/8 (pow.f64 a1 6)) (.f64 -1/8 (pow.f64 a1 6))) (cos.f64 th))) (pow.f64 a2 4)))))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 (.f64 a1 a1) (cos.f64 th)) (.f64 (.f64 a2 a2) (cos.f64 th)))) (/.f64 (sqrt.f64 1/2) (/.f64 (.f64 a1 a1) (.f64 (.f64 (pow.f64 a2 4) 0) (cos.f64 th)))))
(fma.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (.f64 (/.f64 (sqrt.f64 1/2) a1) (/.f64 (.f64 (cos.f64 th) 0) a1)))
(fma.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) 0)
(pow.f64 a2 2)
(*.f64 a2 a2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (.f64 (+.f64 (.f64 -1 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6))))) (.f64 5/64 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a1 8)) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))
(fma.f64 (fma.f64 -1 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))) (/.f64 5/64 (pow.f64 a2 6))) (pow.f64 a1 8) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(fma.f64 (-.f64 (/.f64 5/64 (pow.f64 a2 6)) (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6)))) (pow.f64 a1 8) (fma.f64 a2 a2 (*.f64 a1 a1)))
(fma.f64 (+.f64 (-.f64 (/.f64 5/64 (pow.f64 a2 6)) (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2)) (/.f64 -1/16 (pow.f64 a2 6))) (pow.f64 a1 8) (fma.f64 a2 a2 (*.f64 a1 a1)))
(pow.f64 a1 2)
(*.f64 a1 a1)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (.f64 -1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a2 2) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (pow.f64 a1 2))))
(fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (fma.f64 1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (.f64 a1 a1))))
(fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a2 a2 (fma.f64 a1 a1 (.f64 1/4 (/.f64 (pow.f64 a2 4) (*.f64 a1 a1))))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a2 2) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a1 2) (.f64 1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4))))))))
(fma.f64 -1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (+.f64 (fma.f64 1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (.f64 a1 a1)) (*.f64 1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4)))))))
(fma.f64 -1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a2 a2 (fma.f64 1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a1 a1 (/.f64 (*.f64 (pow.f64 a2 6) 1/8) (pow.f64 a1 4)))))))
(pow.f64 a1 2)
(*.f64 a1 a1)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (.f64 -1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a2 2) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (pow.f64 a1 2))))
(fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (fma.f64 1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (.f64 a1 a1))))
(fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a2 a2 (fma.f64 a1 a1 (.f64 1/4 (/.f64 (pow.f64 a2 4) (*.f64 a1 a1))))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a2 2) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a1 2) (.f64 1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4))))))))
(fma.f64 -1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (+.f64 (fma.f64 1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (.f64 a1 a1)) (*.f64 1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4)))))))
(fma.f64 -1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a2 a2 (fma.f64 1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a1 a1 (/.f64 (*.f64 (pow.f64 a2 6) 1/8) (pow.f64 a1 4)))))))
(pow.f64 a1 2)
(*.f64 a1 a1)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a2 2) (+.f64 (.f64 (+.f64 (.f64 -1 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 a1 6))) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2))) (.f64 5/64 (/.f64 1 (pow.f64 a1 6)))) (pow.f64 a2 8)) (pow.f64 a1 2)))
(+.f64 (.f64 a2 a2) (fma.f64 (fma.f64 -1 (+.f64 (/.f64 1/16 (pow.f64 a1 6)) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2)) (/.f64 5/64 (pow.f64 a1 6))) (pow.f64 a2 8) (.f64 a1 a1)))
(fma.f64 a2 a2 (fma.f64 a1 a1 (*.f64 (pow.f64 a2 8) (-.f64 (/.f64 5/64 (pow.f64 a1 6)) (+.f64 (/.f64 1/16 (pow.f64 a1 6)) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2))))))
(fma.f64 a2 a2 (fma.f64 a1 a1 (*.f64 (pow.f64 a2 8) (-.f64 (+.f64 (/.f64 5/64 (pow.f64 a1 6)) (/.f64 -1/16 (pow.f64 a1 6))) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2)))))
(pow.f64 a2 2)
(*.f64 a2 a2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(fma.f64 1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (fma.f64 -1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(+.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (/.f64 (pow.f64 a1 4) (*.f64 a2 a2)) 0))
(+.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) 0)
(+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (.f64 1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4))))))))
(fma.f64 1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (fma.f64 -1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (+.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4)))))))
(fma.f64 1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (fma.f64 -1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (fma.f64 a2 a2 (fma.f64 a1 a1 (*.f64 1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4))))))))
(pow.f64 a2 2)
(*.f64 a2 a2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(fma.f64 1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (fma.f64 -1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(+.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (/.f64 (pow.f64 a1 4) (*.f64 a2 a2)) 0))
(+.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) 0)
(+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (.f64 1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4))))))))
(fma.f64 1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (fma.f64 -1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (+.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4)))))))
(fma.f64 1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (fma.f64 -1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (fma.f64 a2 a2 (fma.f64 a1 a1 (*.f64 1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4))))))))
a2
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2)
(fma.f64 1/2 (/.f64 (*.f64 a1 a1) a2) a2)
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2))
(fma.f64 -1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3)) (fma.f64 1/2 (/.f64 (*.f64 a1 a1) a2) a2))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5))) a2)))
(fma.f64 -1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3)) (fma.f64 1/2 (/.f64 (*.f64 a1 a1) a2) (fma.f64 1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5)) a2)))
a1
(+.f64 a1 (*.f64 1/2 (/.f64 (pow.f64 a2 2) a1)))
(+.f64 a1 (.f64 1/2 (/.f64 (.f64 a2 a2) a1)))
(fma.f64 1/2 (/.f64 a2 (/.f64 a1 a2)) a1)
(+.f64 a1 (+.f64 (.f64 -1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))) (.f64 1/2 (/.f64 (pow.f64 a2 2) a1))))
(+.f64 a1 (fma.f64 -1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3)) (.f64 1/2 (/.f64 (.f64 a2 a2) a1))))
(+.f64 a1 (fma.f64 1/2 (/.f64 a2 (/.f64 a1 a2)) (*.f64 -1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3)))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5))) (+.f64 a1 (+.f64 (.f64 -1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))) (*.f64 1/2 (/.f64 (pow.f64 a2 2) a1)))))
(fma.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5)) (+.f64 a1 (fma.f64 -1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3)) (.f64 1/2 (/.f64 (.f64 a2 a2) a1)))))
(+.f64 (fma.f64 1/2 (/.f64 a2 (/.f64 a1 a2)) (*.f64 -1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3)))) (fma.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5)) a1))
(*.f64 -1 a1)
(neg.f64 a1)
(+.f64 (.f64 -1 a1) (.f64 -1/2 (/.f64 (pow.f64 a2 2) a1)))
(fma.f64 -1 a1 (.f64 -1/2 (/.f64 (.f64 a2 a2) a1)))
(fma.f64 -1/2 (/.f64 a2 (/.f64 a1 a2)) (neg.f64 a1))
(+.f64 (.f64 -1 a1) (+.f64 (.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))) (*.f64 -1/2 (/.f64 (pow.f64 a2 2) a1))))
(fma.f64 -1 a1 (fma.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3)) (.f64 -1/2 (/.f64 (.f64 a2 a2) a1))))
(-.f64 (fma.f64 -1/2 (/.f64 a2 (/.f64 a1 a2)) (*.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3)))) a1)
(+.f64 (.f64 -1 a1) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))) (.f64 -1/2 (/.f64 (pow.f64 a2 2) a1)))))
(fma.f64 -1 a1 (fma.f64 -1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5)) (fma.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3)) (.f64 -1/2 (/.f64 (.f64 a2 a2) a1)))))
(-.f64 (fma.f64 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5)) -1/16 (fma.f64 -1/2 (/.f64 a2 (/.f64 a1 a2)) (*.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))))) a1)
a1
(+.f64 a1 (*.f64 1/2 (/.f64 (pow.f64 a2 2) a1)))
(+.f64 a1 (.f64 1/2 (/.f64 (.f64 a2 a2) a1)))
(fma.f64 1/2 (/.f64 a2 (/.f64 a1 a2)) a1)
(+.f64 a1 (+.f64 (.f64 -1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))) (.f64 1/2 (/.f64 (pow.f64 a2 2) a1))))
(+.f64 a1 (fma.f64 -1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3)) (.f64 1/2 (/.f64 (.f64 a2 a2) a1))))
(+.f64 a1 (fma.f64 1/2 (/.f64 a2 (/.f64 a1 a2)) (*.f64 -1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3)))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5))) (+.f64 a1 (+.f64 (.f64 -1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))) (*.f64 1/2 (/.f64 (pow.f64 a2 2) a1)))))
(fma.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5)) (+.f64 a1 (fma.f64 -1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3)) (.f64 1/2 (/.f64 (.f64 a2 a2) a1)))))
(+.f64 (fma.f64 1/2 (/.f64 a2 (/.f64 a1 a2)) (*.f64 -1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3)))) (fma.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5)) a1))
a2
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2)
(fma.f64 1/2 (/.f64 (*.f64 a1 a1) a2) a2)
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2))
(fma.f64 -1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3)) (fma.f64 1/2 (/.f64 (*.f64 a1 a1) a2) a2))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5))) a2)))
(fma.f64 -1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3)) (fma.f64 1/2 (/.f64 (*.f64 a1 a1) a2) (fma.f64 1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5)) a2)))
(*.f64 -1 a2)
(neg.f64 a2)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 a1 2) a2)) (.f64 -1 a2))
(fma.f64 -1/2 (/.f64 (*.f64 a1 a1) a2) (neg.f64 a2))
(-.f64 (.f64 -1/2 (/.f64 (.f64 a1 a1) a2)) a2)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 a1 2) a2)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))) (*.f64 -1 a2)))
(fma.f64 -1/2 (/.f64 (*.f64 a1 a1) a2) (fma.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3)) (neg.f64 a2)))
(-.f64 (fma.f64 -1/2 (/.f64 (.f64 a1 a1) a2) (.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3)))) a2)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 a1 2) a2)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5))) (.f64 -1 a2))))
(fma.f64 -1/2 (/.f64 (*.f64 a1 a1) a2) (fma.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3)) (fma.f64 -1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5)) (neg.f64 a2))))
(fma.f64 -1/2 (/.f64 (.f64 a1 a1) a2) (-.f64 (fma.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3)) (.f64 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5)) -1/16)) a2))

prune181.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	196	2	198
Fresh	2	4	6
Picked	0	1	1
Done	1	0	1
Total	199	7	206

Error

Counts

206 → 7

Alt Table

Status	Error	Program
	0.6b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
	0.5b	(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
	0.4b	(*.f64 (cos.f64 th) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
	0.4b	(+.f64 0 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th))))
	0.6b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))))
▶	0.4b	(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))

Compiler

Compiled 5871 to 4071 computations (30.7% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
✓	0.4b	(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))

series11.0ms (0.2%)

Counts

2 → 72

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	th	@	0	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
1.0ms	a2	@	0	(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
1.0ms	th	@	inf	(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
1.0ms	th	@	-inf	(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
1.0ms	a2	@	inf	(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))

rewrite44.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

906×	`log1p-expm1-u_binary64`
906×	`expm1-log1p-u_binary64`
108×	`add-sqr-sqrt_binary64`
105×	`*-un-lft-identity_binary64`
105×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	218	29
2	2512	29

Stop Event

1×	node limit

Counts

2 → 32

Calls

Call 1

Inputs
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (*.f64 (cos.f64 th) (sqrt.f64 1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (*.f64 (cos.f64 th) (sqrt.f64 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (*.f64 (cos.f64 th) (sqrt.f64 1/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 1/2 1/4) (*.f64 (sqrt.f64 (cos.f64 th)) (hypot.f64 a2 a1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/2 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (*.f64 (cos.f64 th) (sqrt.f64 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (*.f64 (cos.f64 th) (sqrt.f64 1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 1/2 (sqrt.f64 1/2)) (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 3) (*.f64 1/2 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 a2 a2) (cos.f64 th)) (*.f64 (*.f64 a1 a1) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)) (*.f64 (cos.f64 th) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (cos.f64 th)) (hypot.f64 a2 a1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (pow.f64 (hypot.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 3) (pow.f64 (cos.f64 th) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 1))))))

simplify52.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

487×	`unswap-sqr_binary64`
433×	`*-commutative_binary64`
414×	`fma-def_binary64`
360×	`distribute-rgt-in_binary64`
353×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	1568
1	152	1262
2	505	1194
3	2207	1164
4	4532	1164

Stop Event

1×	node limit

Counts

104 → 62

Calls

Call 1

Inputs
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)))) (+.f64 (.f64 -1/720 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(*.f64 (pow.f64 a1 2) (cos.f64 th))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(*.f64 (pow.f64 a1 2) (cos.f64 th))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(*.f64 (pow.f64 a1 2) (cos.f64 th))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (.f64 -1/2 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/2 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2))) (.f64 1/24 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4))))))
(+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/2 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2))) (+.f64 (.f64 1/24 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4))) (.f64 -1/720 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)))))))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))

Outputs
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (.f64 a1 a1) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (.f64 a1 a1) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (.f64 a1 a1) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 th th))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
(fma.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 th th)) (.f64 (sqrt.f64 1/2) -1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 th (.f64 th -1/2)) 1) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (+.f64 1 (.f64 th (*.f64 th -1/2)))))
(+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(fma.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (pow.f64 th 4))) (fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 th th))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
(fma.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (pow.f64 th 4))) (fma.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 th th)) (*.f64 (sqrt.f64 1/2) -1/2))))
(fma.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (+.f64 (.f64 th (.f64 th -1/2)) (*.f64 1/24 (pow.f64 th 4))))))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (+.f64 (.f64 th (.f64 th -1/2)) (+.f64 1 (.f64 1/24 (pow.f64 th 4))))))
(+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)))) (+.f64 (.f64 -1/720 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))))
(fma.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (pow.f64 th 4))) (fma.f64 -1/720 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (pow.f64 th 6))) (fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 th th))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))))
(fma.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (pow.f64 th 4))) (fma.f64 -1/720 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (pow.f64 th 6))) (fma.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 th th)) (.f64 (sqrt.f64 1/2) -1/2)))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 th (.f64 th -1/2)) 1) (fma.f64 a1 a1 (.f64 a2 a2)))) (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (+.f64 (.f64 1/24 (pow.f64 th 4)) (.f64 -1/720 (pow.f64 th 6))))))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (fma.f64 a2 a2 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (+.f64 (.f64 th (.f64 th -1/2)) (+.f64 (.f64 -1/720 (pow.f64 th 6)) (*.f64 1/24 (pow.f64 th 4))))))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (.f64 a1 a1) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (pow.f64 a1 2) (cos.f64 th))
(.f64 (.f64 a1 a1) (cos.f64 th))
(.f64 a1 (.f64 a1 (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (cos.f64 th) (.f64 a2 a2))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (cos.f64 th) (.f64 a2 a2))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (cos.f64 th) (.f64 a2 a2))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(*.f64 (pow.f64 a1 2) (cos.f64 th))
(.f64 (.f64 a1 a1) (cos.f64 th))
(.f64 a1 (.f64 a1 (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(*.f64 (pow.f64 a1 2) (cos.f64 th))
(.f64 (.f64 a1 a1) (cos.f64 th))
(.f64 a1 (.f64 a1 (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a1 a1) (.f64 a2 a2))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (.f64 -1/2 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(+.f64 (.f64 a2 a2) (+.f64 (.f64 a1 a1) (.f64 -1/2 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 th th)))))
(fma.f64 a2 a2 (fma.f64 a1 a1 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (.f64 th th) -1/2))))
(.f64 (+.f64 (.f64 th (.f64 th -1/2)) 1) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (+.f64 1 (.f64 th (.f64 th -1/2))))
(+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/2 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2))) (.f64 1/24 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4))))))
(+.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (fma.f64 -1/2 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 th th)) (.f64 1/24 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (pow.f64 th 4)))))
(fma.f64 a2 a2 (fma.f64 a1 a1 (fma.f64 -1/2 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 th th)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (pow.f64 th 4) 1/24)))))
(fma.f64 a1 a1 (fma.f64 a2 a2 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (+.f64 (.f64 th (.f64 th -1/2)) (*.f64 1/24 (pow.f64 th 4))))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (+.f64 (.f64 th (.f64 th -1/2)) (+.f64 1 (*.f64 1/24 (pow.f64 th 4)))))
(+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/2 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2))) (+.f64 (.f64 1/24 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4))) (.f64 -1/720 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)))))))
(+.f64 (.f64 a2 a2) (+.f64 (.f64 a1 a1) (fma.f64 -1/2 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 th th)) (fma.f64 1/24 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (pow.f64 th 4)) (.f64 (.f64 -1/720 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (pow.f64 th 6))))))
(fma.f64 a2 a2 (fma.f64 a1 a1 (fma.f64 -1/2 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 th th)) (fma.f64 1/24 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (pow.f64 th 4)) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (pow.f64 th 6) -1/720))))))
(+.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (+.f64 (.f64 1/24 (pow.f64 th 4)) (.f64 -1/720 (pow.f64 th 6)))) (.f64 (+.f64 (.f64 th (.f64 th -1/2)) 1) (fma.f64 a1 a1 (.f64 a2 a2))))
(fma.f64 a1 a1 (fma.f64 a2 a2 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (+.f64 (.f64 th (.f64 th -1/2)) (+.f64 (.f64 -1/720 (pow.f64 th 6)) (.f64 1/24 (pow.f64 th 4)))))))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(fma.f64 (cos.f64 th) (.f64 a2 a2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))

prune48.0ms (0.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	62	7	69

Error

Counts

69 → 7

Alt Table

Status	Error	Program
	0.6b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
	0.5b	(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
▶	0.4b	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
	0.6b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))))
	0.4b	(*.f64 (cos.f64 th) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
✓	0.4b	(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))

Compiler

Compiled 1232 to 825 computations (33% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sqrt.f64 1/2) (cos.f64 th))
✓	0.3b	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))

series10.0ms (0.1%)

Counts

2 → 40

Calls

12 calls:

Time	Variable		Point	Expression
5.0ms	th	@	0	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
1.0ms	a1	@	0	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
0.0ms	th	@	inf	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
0.0ms	th	@	-inf	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
0.0ms	a2	@	0	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))

rewrite43.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

902×	`log1p-expm1-u_binary64`
902×	`expm1-log1p-u_binary64`
108×	`add-sqr-sqrt_binary64`
105×	`*-un-lft-identity_binary64`
105×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	218	25
2	2506	25

Stop Event

1×	node limit

Counts

2 → 32

Calls

Call 1

Inputs
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 a1 a1) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (*.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (*.f64 a1 a1)) (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) (pow.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) 3) (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/2 (pow.f64 (cos.f64 th) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 1/2 (sqrt.f64 1/2)) (pow.f64 (cos.f64 th) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 3) (*.f64 1/2 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 1))))))

simplify33.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

451×	`associate-+l+_binary64`
379×	`*-commutative_binary64`
352×	`associate-+r+_binary64`
337×	`fma-def_binary64`
297×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	1024
1	146	820
2	438	774
3	1885	746

Stop Event

1×	node limit

Counts

72 → 54

Calls

Call 1

Inputs
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)))) (+.f64 (.f64 -1/720 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(sqrt.f64 1/2)
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (sqrt.f64 1/2))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (pow.f64 th 4))) (sqrt.f64 1/2)))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (pow.f64 th 4))) (+.f64 (sqrt.f64 1/2) (.f64 -1/720 (.f64 (sqrt.f64 1/2) (pow.f64 th 6))))))

Outputs
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a2 a2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
(.f64 a2 (.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a1 a1)))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a1 a1)))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a1 a1)))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a2 a2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
(.f64 a2 (.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a2 a2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
(.f64 a2 (.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) -1/2)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (fma.f64 (sqrt.f64 1/2) (.f64 th (.f64 th -1/2)) (sqrt.f64 1/2)))
(+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(fma.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (pow.f64 th 4))) (fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
(fma.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (pow.f64 th 4))) (fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 th th)) -1/2))))
(fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/24 (pow.f64 th 4)) (.f64 th (*.f64 th -1/2))))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 th (.f64 th -1/2)) (+.f64 1 (.f64 1/24 (pow.f64 th 4))))))
(+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)))) (+.f64 (.f64 -1/720 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))))
(fma.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (pow.f64 th 4))) (fma.f64 -1/720 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (pow.f64 th 6))) (fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(fma.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (pow.f64 th 4))) (fma.f64 -1/720 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (pow.f64 th 6))) (fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) -1/2)))))
(+.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (fma.f64 (sqrt.f64 1/2) (.f64 th (.f64 th -1/2)) (sqrt.f64 1/2))) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/24 (pow.f64 th 4)) (*.f64 -1/720 (pow.f64 th 6))))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (+.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 th (.f64 th -1/2)) (+.f64 (.f64 1/24 (pow.f64 th 4)) (*.f64 -1/720 (pow.f64 th 6)))))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (.f64 (*.f64 a2 a2) (cos.f64 th))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(sqrt.f64 1/2)
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (sqrt.f64 1/2))
(fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 th th)) (sqrt.f64 1/2))
(fma.f64 -1/2 (.f64 (.f64 (sqrt.f64 1/2) th) th) (sqrt.f64 1/2))
(fma.f64 (sqrt.f64 1/2) (.f64 th (.f64 th -1/2)) (sqrt.f64 1/2))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (pow.f64 th 4))) (sqrt.f64 1/2)))
(fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 th th)) (fma.f64 1/24 (*.f64 (sqrt.f64 1/2) (pow.f64 th 4)) (sqrt.f64 1/2)))
(fma.f64 -1/2 (.f64 (.f64 (sqrt.f64 1/2) th) th) (fma.f64 1/24 (*.f64 (sqrt.f64 1/2) (pow.f64 th 4)) (sqrt.f64 1/2)))
(+.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/24 (pow.f64 th 4)) (.f64 th (.f64 th -1/2)))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 th (.f64 th -1/2)) (+.f64 1 (.f64 1/24 (pow.f64 th 4)))))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (pow.f64 th 4))) (+.f64 (sqrt.f64 1/2) (.f64 -1/720 (.f64 (sqrt.f64 1/2) (pow.f64 th 6))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 th th)) (fma.f64 1/24 (.f64 (sqrt.f64 1/2) (pow.f64 th 4)) (+.f64 (sqrt.f64 1/2) (.f64 -1/720 (*.f64 (sqrt.f64 1/2) (pow.f64 th 6))))))
(fma.f64 -1/2 (.f64 (.f64 (sqrt.f64 1/2) th) th) (fma.f64 1/24 (.f64 (sqrt.f64 1/2) (pow.f64 th 4)) (fma.f64 -1/720 (.f64 (sqrt.f64 1/2) (pow.f64 th 6)) (sqrt.f64 1/2))))
(+.f64 (fma.f64 (sqrt.f64 1/2) (.f64 -1/720 (pow.f64 th 6)) (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/24 (pow.f64 th 4)) (.f64 th (*.f64 th -1/2)))))
(+.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 th (.f64 th -1/2)) (+.f64 (.f64 1/24 (pow.f64 th 4)) (*.f64 -1/720 (pow.f64 th 6))))))

prune42.0ms (0.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	54	7	61

Error

Counts

61 → 7

Alt Table

Status	Error	Program
	0.6b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
	0.5b	(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
✓	0.4b	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
	0.6b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))))
	0.4b	(*.f64 (cos.f64 th) (fma.f64 (/.f64 a1 (sqrt.f64 2)) a1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
✓	0.4b	(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))

Compiler

Compiled 1049 to 664 computations (36.7% saved)

regimes382.0ms (5.7%)

Accuracy

Total 0.4b remaining (90.3%)

Threshold costs 0.4b (90.3%)

Counts

74 → 1

Compiler

Compiled 965 to 567 computations (41.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	13	18

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))

Outputs
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))

end113.0ms (1.7%)

Stop Event

1×

fuel

Remove

(sort a1 a2)

Compiler

Compiled 169 to 122 computations (27.8% saved)

Details

analyze1.1s (16.4%)

sample4.2s (63%)

preprocess25.0ms (0.4%)

simplify9.0ms (0.1%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series15.0ms (0.2%)

rewrite45.0ms (0.7%)

simplify44.0ms (0.7%)

prune78.0ms (1.2%)

localize9.0ms (0.1%)

series32.0ms (0.5%)

rewrite48.0ms (0.7%)

simplify81.0ms (1.2%)

prune181.0ms (2.7%)

localize8.0ms (0.1%)

series11.0ms (0.2%)

rewrite44.0ms (0.7%)

simplify52.0ms (0.8%)

prune48.0ms (0.7%)

localize8.0ms (0.1%)

series10.0ms (0.1%)

rewrite43.0ms (0.6%)

simplify33.0ms (0.5%)

prune42.0ms (0.6%)

regimes382.0ms (5.7%)

simplify3.0ms (0.1%)

end113.0ms (1.7%)

Profiling